scholarly journals Computation of a Canonical Form for Linear 2D Systems

2014 ◽  
Vol 2014 ◽  
pp. 1-6 ◽  
Author(s):  
Mohamed Salah Boudellioua
Keyword(s):  
State Space ◽  
Linear Systems ◽  
Canonical Form ◽  
Polynomial Matrix ◽  
2D Systems ◽  
Space Systems ◽  
Polynomial Matrices ◽  
Computational Aspects ◽  
State Space Systems ◽  
Linear State

Symbolic computation techniques are used to obtain a canonical form for polynomial matrices arising from discrete 2D linear state-space systems. The canonical form can be regarded as an extension of the companion form often encountered in the theory of 1D linear systems. Using previous results obtained by Boudellioua and Quadrat (2010) on the reduction by equivalence to Smith form, the exact connection between the original polynomial matrix and the reduced canonical form is set out. An example is given to illustrate the computational aspects involved.

scholarly journals Reduction of second order linear dynamical systems, with large dissipation, by state variable transformations

1990 ◽  
Vol 32 (2) ◽  
pp. 207-222
Author(s):  
R. B. Leipnik
Keyword(s):  
Dynamical Systems ◽  
State Space ◽  
Computing Time ◽  
Square Root ◽  
Space Systems ◽  
Linear Dynamical Systems ◽  
State Variable ◽  
State Space Systems ◽  
Linear State ◽  
Eigenvectors And Eigenvalues

AbstractLinear dynamical systems of the Rayleigh form are transformed by linear state variable transformations , where A and B are chosen to simplify analysis and reduce computing time. In particular, A is essentially a square root of M, and B is a Lyapunov quotient of C by A. Neither K nor C is required to be symmetric, nor is C small. The resulting state-space systems are analysed by factorisation of the evolution matrices into reducible factors. Eigenvectors and eigenvalues are determined by these factors. Conditions for further simplification are derived in terms of Kronecker determinants. These results are compared with classical reductions of Rayleigh, Duncan, and Caughey, which are reviewed at the outset.

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